A lot of sentences. Could you check each of them? Thank you in advance.

난 어제 상을 받았어 - I got an award yesterday
난 어제 편지를 받았어 - I got a letter yesterday
난 벌을 받았어 - I got a punishment

미안.. ....어머니가 나한테 벌을 주셨어. 그래서, 나는 밖에 못 나가 
Mum gave me punishment, so I can't go out. Sorry...

크리스마스 선물을 많이 받았다 - I got a lot of Christmas gifts
1년 전에는 생밀 선물을 받지 못했어 - I didn't get a birthday gift/present year ago
할아버지께서(you don't need to say 는) 월요일에 연금을 받으셨어요- My grandfather received a pension/annuity on Monday

(i didn't know what 번연히 means before seeing your writing, so i searched it, and i found out the meaning of 번연히. I would say we don't use 번연히. but someone use this and they use this as meaning of obviously. To say this kinda thing, we use 뻔히 meaning too obviously. and also suddenly = 갑자기)

문제의 심각성을 갑자기 깨달았다 - I suddenly realized the magnitude of a problem 

그녀는 갑자기 빠르게 달렸어 - She suddenly ran fast
그는 갑자기(갑작스럽게 also works. in a kinda hard way to say this, 느닷없이) 문을 닫았어- He suddenly closed the door
그는 갑자기 문을 열었어- He suddenly opened the door
내가 취직했어 or 직장을 얻었어 - I got a job/I found a job

내 미식 축구팀이 골을 넣었어요 or 내 미식 축구팀이 득점을 했어요- My football team scored a goal
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재미있는 책에 대해 상을 받았어요 - I got an award for an interesting book
불렀던 노래에 대해 상을 받았어요 - I got an award for a song I sang

(I am not sure how to write cathegory or what for I got an award. What are possible examples? )
______에 대해 상을 받았어요 ?

you can just say 노래를 잘 불러서 상을 받았어요 

or 그때 불렀던 노래 덕분에 상을 받았어요. (덕분에 is almost the same as 때문에, but you have to say positive things in front of 덕분에)

GOOD~ CLOSE ENOUGH. KEEP TRYING~